# Difference b/w Combinations of random variables and transforms of rv's.

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#1
Hey there (:

Can someone briefly explain to me the difference b/w combinations of random variables and transforms of random variables (as far as I know, only "combinations of rv's" is included interest Edexcel's A Level Math S4 module but I'm just curious).

Also, the topic is explained as : "distribution of linear combinations of independent normal random variables". So I was wondering, why is "linear" mentioned there? What is 'linear' about the distribution of the said combinations of independent normal rv's?

Thank you very much! (:

PS : I haven't given this much thought & I won't be able to research about it either since I'm running out of time (will be travelling soon) and I need to clarify my doubts faster. Hence, the post here, on TSR. Under normal circumstances, I'd have tried to find out for myself by researching about it online and post on TSR only if I wasn't able to get answers even then)
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7 years ago
#2
(Original post by Sidhant Shivram)
Hey there (:

Can someone briefly explain to me the difference b/w combinations of random variables and transforms of random variables (as far as I know, only "combinations of rv's" is included interest Edexcel's A Level Math S4 module but I'm just curious).
Roughly speaking, a transformation of random variables is given by some function of the random variables, such as or etc etc, where are suitable R.V.s.

I've never heard the phrase "combination of r.v.s" but I'd say it's reasonable to assume that it is the same thing as a transformation. A linear combination, on the other hand, is a more specific type of transformation.

Also, the topic is explained as : "distribution of linear combinations of independent normal random variables". So I was wondering, why is "linear" mentioned there? What is 'linear' about the distribution of the said combinations of independent normal rv's?
"Linear" is used to describe the type of transformation that yields a "linear combination" of R.V.s, as opposed to "linearity" of it's distribution (whatever that means).

A transformation of random variables is called linear if , where are suitably chosen constants, and we say that is a linear combination of the .

It's called linear because the random variables appear in a linear fashion (in the same way that represents a straight line in the plane - the are not transformed themselves i.e. is not a linear transformation because has been transformed in a non-linear fashion.)
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#3
(Original post by Farhan.Hanif93)
Roughly speaking, a transformation of random variables is given by some function of the random variables, such as or etc etc, where are suitable R.V.s.

I've never heard the phrase "combination of r.v.s" but I'd say it's reasonable to assume that it is the same thing as a transformation. A linear combination, on the other hand, is a more specific type of transformation.

"Linear" is used to describe the type of transformation that yields a "linear combination" of R.V.s, as opposed to "linearity" of it's distribution (whatever that means).

A transformation of random variables is called linear if , where are suitably chosen constants, and we say that is a linear combination of the .

It's called linear because the random variables appear in a linear fashion (in the same way that represents a straight line in the plane - the are not transformed themselves i.e. is not a linear transformation because has been transformed in a non-linear fashion.)
Oh okay! That makes sense! Thank you so much! (:

Sent from my iPhone
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